2 P. BIELIAVSKY, L. CLAESSENS, D. STERNHEIMER, ANDY. VOGLAIRE

These deformations have important consequences. Introducing a small negative

curvature

p

permits to consider [AFFS] massless particles as composites of more

fundamental objects, the Dirac singletons, so called because they are associated

with unitary irreducible representations (UIR) of 80(2, 3), discovered by Dirac in

1963,

so poor in states that the weight diagram fits on a single line. These have

been called Di and Rae and are in fact massless UIR of the Poincare group in one

space dimension less, uniquely extendible to the corresponding conformal group

80(2,

3)

(AdS4jCFT3 symmetry, a manifestation of 't Hooft's holography). That

kinematical fact was made dynamical [FF88] in a manner consistent with quan-

tum electrodynamics (QED), the photons being considered as 2-Rac states and

the creation and annihilation operators of the naturally confined Rae having un-

usual commutation relations (a kind of "square root" of the canonical commutation

relations for the photon).

Later [FFS] this phenomenon has been linked with the (then very recently)

observed oscillations of neutrinos (see below, neutrino mixing). Shortly after-

wards, making use of flavor symmetry, Fr(llnsdal was able to modify the electroweak

model [Fr!I}OO], obtaining initially massless leptons (see below) that are massified

by Yukawa interaction with Higgs particles. (In this model, 5 pairs of Higgs are

needed and it predicts the existence of new mesons, parallel to the W and Z of the

U(2)-invariant electroweak theory, associated with a U(2) flavor symmetry.)

Quantum groups can be viewed [BGGS] as an avatar of deformation quantiza-

tion when dealing with Hopf algebras. Of particular interest here are the quantized

AdS groups [FHT, Sta98], especially at even root of unity since they have some

finite dimensional UIR, a fact generally associated with compact groups and groups

of transformations of compact spaces. It is then tempting to consider quantized

AdS spaces at even root of unity

q

=

ei6

as "small black holes" in an ambient

Minkowski space that can be obtained as a limit when

pq

--t

-0. Note that, fol-

lowing e.g. 't Hooft (see e.g. [Hoo06] but his approach started around

1980)

that

some form of communication is possible with quantum black holes by interaction

at their surface.

At present, conventional wisdom has it that our universe is made up mostly of

"dark energy" (74% according to a recent Wilkinson Microwave Anisotropy Probe,

WMAP), then of "dark matter" (22% according to WMAP), and only 4% of "our"

ordinary matter, which we can more directly observe. Dark matter is "matter",

not directly observed and of unknown composition, that does not emit nor reflect

enough electromagnetic radiation to be detected directly, but whose presence can

be inferred from gravitational effects on visible matter. According to the Standard

Model, dark matter accounts for the vast majority of mass in the observable uni-

verse. Dark energy is a hypothetical form of energy that permeates all of space. It

is currently the most popular method for explaining recent observations that the

universe appears to be expanding at an accelerating rate, as well as accounting for

a significant portion of the missing mass in the universe.

The Standard Model of particle physics is a model which incorporates three

of the four known fundamental interactions between the elementary particles that

make up all matter (the fourth one, weakest but long range, being gravity).

It

came

after the electroweak theory that incorporated QED (electromagnetic interactions)

associated with the photon and the so-called weak interactions, associated with the

leptons that now exist in three generations (flavors): electron, muon and tau, and